Fusion energy gain factor

Most fusion reactions release at least some of their energy in a form that cannot be captured within the plasma, so a system at Q = 1 will cool without external heating.

With typical fuels, self-heating in fusion reactors is not expected to match the external sources until at least Q ≈ 5.

At this point the reaction becomes self-sustaining, a condition called ignition, and is generally regarded as highly desirable for practical reactor designs.

Additionally, fusion fuels, especially tritium, are very expensive, so many experiments run on various test gasses like hydrogen or deuterium.

In 1955, John Lawson was the first to explore the energy balance mechanisms in detail, initially in classified works but published openly in a now-famous 1957 paper.

In this paper he considered and refined work by earlier researchers, notably Hans Thirring, Peter Thonemann, and a review article by Richard Post.

Expanding on all of these, Lawson's paper made detailed predictions for the amount of power that would be lost through various mechanisms, and compared that to the energy needed to sustain the reaction.

[c] Some amount of this energy, Ploss, is lost through a variety of mechanisms, mostly convection of the fuel to the walls of the reactor chamber and various forms of radiation that cannot be captured to generate power.

In order to keep the reaction going, the system has to provide heating to make up for these losses, where Ploss = Pheat to maintain thermal equilibrium.

The magnetic approaches, MCF for short, are generally designed to operate in the (quasi) steady state.

To do so, ICF devices compress the fuel to extreme conditions, where the self-heating reactions occur very rapidly.

Once set up, the steady state is maintained by injecting heat into the plasma with a variety of devices.

For this reason, Pheat in the steady state is something fairly close to all of the energy being fed into the reactor, and the efficiency of the heating systems is generally ignored.

[6] If one were to use a similar definition of Pheat, that is, all the energy being fed into the system, then ICF devices are hopelessly inefficient.

[7][8] ICF proponents point out that alternative "drivers" could be used that would improve this ratio at least ten times.

Thus, it is typical to define Pheat for ICF devices as the amount of driver energy actually hitting the fuel, about 2 MJ in the case of NIF.

To make this distinction clear, modern works often refer to this definition as scientific breakeven, Qsci or sometimes Qplasma, to contrast it with similar terms.

[11] In order to lower costs, many experimental machines are designed to run on test fuels of hydrogen or deuterium alone, leaving out the tritium.

In this case, the basic definition changes by adding additional terms to the Pfus side to consider the efficiencies of these processes.

This means that only the charged particles from the reactions can be captured within the fuel mass and give rise to self-heating.

Due to various exothermic and endothermic reactions, the blanket may have a power gain factor MR. MR is typically on the order of 1.1 to 1.3, meaning it produces a small amount of energy as well.

[15] Thus, the fusion energy gain factor required to reach engineering breakeven is defined as:[16]

Considering real-world losses and efficiencies, Q values between 5 and 8 are typically listed for magnetic confinement devices to reach

Thus, in overall terms, the self-heating process becomes more efficient as the temperature increases, and less energy is needed from external sources to keep it hot.

More importantly, this number is more likely to be near-constant, meaning that further improvements in plasma performance will result in more energy that can be directly used for commercial generation, as opposed to recirculation.

[25] Most fusion reactor designs being studied as of 2017[update] are based on the D-T reaction, as this is by far the easiest to ignite, and is energy-dense.

[13] Lawrence Livermore National Laboratory (LLNL), the leader in ICF research, uses the modified Q that defines Pheat as the energy delivered by the driver to the capsule, as opposed to the energy put into the driver by an external power source.

[29][30] This term was not universally used; other groups adopted the redefinition of Q but continued to refer to Pfus = Plaser simply as breakeven.

[31] On 7 October 2013, LLNL announced that roughly one week earlier, on 29 September, it had achieved scientific breakeven in the National Ignition Facility (NIF).

For this press release, they re-defined Q once again, this time equating Pheat to be only the amount energy delivered to "the hottest portion of the fuel", calculating that only 10 kJ of the original laser energy reached the part of the fuel that was undergoing fusion reactions.